Optimization models are widely used in finance where they are employed primarily in two major portfolio-based applications: Asset Allocation models and Portfolio Construction models. The Asset Allocation models are used to create major strategic allocations for an investment portfolio, such as a pension fund with one or more broad market segments (e.g., equity, fixed income, real estate, cash, etc). The Portfolio Construction models are used to create portfolios consisting of specific securities having very specific implementation constraints and objectives, such as trading efficiency, purchase constraints, etc.
Results generated by the models are typically represented graphically on one or more Efficient Frontier charts, which may simply be line graphs plotted on x-axis (risk) and y-axis (return). With the introduction of mean variance optimization (“MVO”) by Markowitz in early 1950's, it became apparent to practitioners that asset allocation and portfolio optimization procedures frequently produce results that are not practical. Specifically, the results were not diversified enough and tend to relatively overweigh assets having small asset variance and large mean return estimates. Furthermore, the results are not robust, wherein they are very sensitive to measurement error in input parameters such as estimates of asset return means and variance-covariance matrix. Thus, a small change in input parameters could lead to a dramatic shift in both the efficient frontier and efficient allocations.